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The eccentricity of the ellipse if minor axis is equal to the distance between the foci is Answer is 1 radical 2 how?
SohaQureshigp5908
The standard equation for an ellipse centered at the origin is [x2/a2] + [y2/b2] = 1
We also have the relationship, b2 = a2 - c2 where c is the distance of the foci from the centre and a & b are the half lengths of the major and minor axes respectively.
When the length of the minor axis equals the distance between the two foci then 2b = 2c : b = c.
Thus, a2 =b2 + c2 = 2b2
One of the formulae for the eccentricity of an ellipse is, e = √[(a2 - b2)/a2]
Thus, e = √[(2b2 - b2) / 2b2] = √½ = 1/√2.
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